Let's discuss your scenarios point by point.
people start posting answers EVEN AFTER AN ACCEPT
This is perfectly normal. As long as the new answer answers the question, it is permitted even if it is posted a year later. Late answers are sometimes the best answers.
or post comments that go off topic
Off-topic comments that are not offensive can either be responded too by saying that it is not relevant to the question or the answer or it can simply be ignored. If it is offensive, flag the comment.
or challenge the answer (usually erroneously)
Challenging the answer is an essential part of the system. However, the answerer is not obligated to respond to comments. Nor is the questioner obligated to justify the accepted answer. If the comments are not courteous and not relevant to the question, flag the comment.
or things just get out of hand with random discussion
If random comments are occurring between two parties other than the questioner and the answerers, flag the comments.
The bottom line is that there is a difference between annoying and offensive. When annoying things happen in questions that you participate in, it makes it less enjoyable to ask or answer questions. But even when this happens, what is annoying to you is less annoying to people who can benefit from the question and its answers. They skim over the annoying parts and aren't bothered by them.
It's easy to say but just try to get a thicker skin and if you don't think you can flag anything then just try to let it go and move on to the next question or answer. When you are tempted to reply to a baiting comment, just let it go. It's hard when you want to put somebody in their place but life is too short and you have better things to do.